Modern satellites and other cellular communication systems sometimes achieve a high degree of frequency reuse by employing a number of spot beams rather than a large area single beam. The spot beams provide a beam laydown that forms coverage over a geographic area, and each beam is assigned to operate on a particular orthogonal channel. With this arrangement, two or more beams may reuse the same orthogonal channel through spatial isolation.
Providing spot beam coverage therefore involves assigning orthogonal channels to respective spot beams that provide coverage throughout the geographic area. For instance, these spot beams may be configured in a manner that maintains a desired isolation (e.g., carrier-to-interference ratio) value and minimizes interference among beams. In one parlance, each spot beam may be assigned a spot beam color corresponding to an orthogonal channel. Identical orthogonal channels, then, may be reused by different spot beams with the same spot beam color. By way of example, communication systems may use three, four, or seven different spot beam colors.
For systems with arbitrary geospatial user locations and limited spectral resources, the optimization of coloring to minimize interference among spot beams is fundamentally a solution space that is factorial in size. An exhaustive search for a solution to maximize the minimum carrier-to-interference ratio can be shown to take exponential time on the order of NcNb, where Nc is the number of colors and Nb is the number of beams. For example, in a 4-color reuse system with 100 beams, there are approximately 1.6×1060 solutions. Existing approaches for assigning spot beam colors for systems with arbitrary geospatial user locations and limited spectral resources suffer from excessive runtimes and memory usage. Improvements are therefore desired.